4. Treasury bills, notes, and bonds Suppose you purchase a corporate bond that is due in one year, with a face value of $100 and an annual coupon rate of 6.5%. Coupons are paid at the end of each year. The annual coupon payment is . If the current yield is 5.0%, then the price paid for the bond is . Suppose interest rates increase. The price of your existing corporate bond will .

A bond is a fixed income security. The issuer of the bond has to pay a fixed amount to the holder of the bond every period. These payments are known as coupon payments and calculated based on the contractual coupon rate and the face value of the bond. In this case, the coupon payments amount to 6.5% (0.065) * $100 = $6.05.

A bond's price is the present value of all future anticipated cash flows. To calculate this, the prevailing market interest rate or yield (5%) is used to discount the cash flows. Since the period is only one year and the coupon rate is annual, the repayment of the face value of the bond will coincide with the coupon payment. At the end of the year $106.5 ($100 (face value) + $6.5(coupon) will be paid out. The discounting of this amount is as follows:

Present value (bond price) = Future Value/(1 + yield)^1

$101.4285714 = $106.5/(1+0.05)^1 where the numerator is the total amount paid at year end and the denominator is the discounting factor raised to the power of 1 to signify the duration of one time period or a year.

Interest rates and bond prices have an inverse relationship. The higher the interest rate, the lower the bond price and vice versa. Using the formula above, if the yield was lower than 5%, say 3% then the bond price would be $103.4 but if the yield was higher than 5%, say 7% then the bond price would be $99.53